I am not sure if you are speaking from your knowledge of Eastern culture, Chris, but it doesn't really make sense to me that it would alleviate grief. I'd grieve even more knowing that that potential was there but was never truly developed (as it is in most cases).
There is a Mahayana teaching that everyone is moving towards enlightenment at the pace they are capable of. This might help. But I may be misunderstanding.
To me, the teachings on Buddha Nature are an encouragement that it is possible to attain enlightenment (because I already have it, as it were), to seek nowhere else and to let go of what is false and unwholesome, rather than accrue more. It is also a pointer not to set up false dualities and learn to see the perfect aspect of everything including myself.
The concept of Buddha nature is often used interchangeably with Nibbana (Nirvana) which is hardly ever mentioned in Zen. Mind you Buddha nature is not mentioned all that often since not even a dog has it...